New to astrophysics, don't have a good physics foundation, need some help

[Aurealis]

Hi everyone,

So I have always been interested in space, and when my college offered an intro to astrophysics course with no prerequisites, I jumped at the opportunity. I had already had a lower level astronomy/physics course, and physics and astronomy in high school, so I thought I'd be fine, but am now finding that everything is a much bigger struggle than presupposed! I learn quickly and just need to find access to some basic concepts, as my grasping at remenants from high school physics is not really getting me anywhere.

Here is a problem that I understand loosely how to set up, but I don't quite know which formula to use or which values to put where:

An astronaut in a starship travel to a Centauri, a distance of approximately 4 ly as measured from Earth, at a speed of u/c=0.8.

d.) A radio signal is sent from Earth to the starship every 6 months, as measured by a clock on Earth. What is the time interval between reception of one of these signals and reception of the next signal aboard the starship?

In previous parts of the problem I solved that the trip to "a Centauri" takes 5 years, as measure by a clock on Earth, 3 years, measured by the pilot, and the distance between the two measured by the pilot was 2.4 ly.

Now, I realize that I need to figure out how long it will take a radiowave to the starship at distance A, then how far the starship travels in 6 months, then how long it will take a radiowave to travel distance B. Radiowaves travel at the speed of light, and the starship is traveling at a speed of u/c=0.8. I believe I need to use some manipulation of the formula:

y=1/(sqrt(1-(u^2)/(c^2))) (excuse the "y" instead of the appropriate symbol, working with a keyboard, you know how it goes)

But I am just not sure how to manipulate, or what exactly to put where...and I'm sure it's an extremely intuitive problem, I'm just messing up/not seeing little things. Any help would be appreciated! Also if anyone has any helpful facts about online astrophysics tutoring, or anything, please let me know!

 

[qraal]

Hi everyone,

Here is a problem that I understand loosely how to set up, but I don't quite know which formula to use or which values to put where:

An astronaut in a starship travel to a Centauri, a distance of approximately 4 ly as measured from Earth, at a speed of u/c=0.8.

d.) A radio signal is sent from Earth to the starship every 6 months, as measured by a clock on Earth. What is the time interval between reception of one of these signals and reception of the next signal aboard the starship?

Any help would be appreciated! Also if anyone has any helpful facts about online astrophysics tutoring, or anything, please let me know!

Hi Aurealis

If you draw a Minkowski diagram for the ship and the Earth reference frames, then the answers appear graphically. The y-axis is Earth-time, the x-axis is space, and light moves in lines at 45 degrees to the y-axis. To move at 0.8c the ship-line rises 5 units for every 4 along the x-axis. An even number of ticks up the y-axis marks the six-month Earth time-steps, 10 in total. The first one at six months leaves when the ship is at 0.8*0.5 light years out, assuming instant acceleration. To work out their intercept let's look at the two lines, light and ship.

Light moves with a slope of 1, and the first pulse's origin is at x=0, y=0.5 (in light-years & years.) Thus y = x + 0.5

Ship moves with a slope of 1.25, thus...

y = 1.25x

They intercept at where the equality holds true...

x + 0.5 = 1.25x

i.e. x = 2, and so y = 2.5

...and so forth for the rest of the pulses. One problem is that some pulses won't be received until after the ship has arrived and presumably stopped moving with respect to Earth (approximately so since Alpha Cen moves w.r.t. Earth.) In that case the ship's time returns to being a vertical line, but 4 light years away from the Earth axis and starting at y = 5.

The ship board clock (y') measures the ticks to arrive at 0.6 times the Earth clock time-span, thus the first arrives after (0.6*2.5) = 1.5 years, the next at x = 4, thus y' = 3 years. Back on Earth, the year 3 time-pulse from the ship's clock wouldn't arrive until 9 years after the ship set out. The so-called "Twin Paradox" isn't apparent until the ship and Earth have returned to each other's proximity, at y=10 & y'=6 if the ship returned to Earth immediately after arrival at Alpha Centauri at the same speed. Then the mismatch becomes apparent.

If we naively derived the ship's average speed by dividing the distance to Alpha Centauri by the time-pulses received by the ship from Earth, then the speed would be 4 times lightspeed. But this is an unphysical "speed", akin to the super-luminal pulses seen emitting from some Quasars.

 

[Aurealis]

Thank you!

 

[Aurealis]

So, another question. I need to determine photons/m^2, and I have wavelength and flux. exact problem reads:

Using the peak emission wavelength of Sirius A as an estimate of the average wavelength and assuming that the flux is reduced by a factor of two due to atmospheric absorption, determine the number of photons/m^2

Any help is EXTREMELY appreciated!

 

[qraal]

So, another question. I need to determine photons/m^2, and I have wavelength and flux. exact problem reads:

Using the peak emission wavelength of Sirius A as an estimate of the average wavelength and assuming that the flux is reduced by a factor of two due to atmospheric absorption, determine the number of photons/m^2

Any help is EXTREMELY appreciated!

Depends on the luminosity of Sirius assumed and the distance one is computing the number of photons/m^2. What figures do you have?

 

[Aurealis]

Shoot, I had...flux, absolute bolometric magnitude, and luminosity i think? I think I ended up dividing wavelength by the speed of light, and then multiplying the...flux by that time I think? Yes. Is that right? It was for a take home test that I already turned in, but I still want to know how to actually do the problem, since I'll have to do more like it later!

 

[qraal]

If you know the flux (J/m^2) then you need to know the energy per photon (E = hc/λ) and then divide the flux by the photon energy, after you work out the peak wavelength (λ_max = b/T) where b is the Wien's displacement constant (2.898E-3 m.K) and T is the temperature of the emitting source (Sirius A in this case.) Sounds like you've come close, but Planck's constant is needed somewhere in the mix.

 

[Aurealis]

Thank you, that was very helpful!